Digital Logic and Number Base Conversion Concepts

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Questions and Answers

When converting a decimal number to base-r using the remainder method, what condition signifies the termination of the successive division?

When the remainder is 0

When the quotient is 1

When the quotient is 0 (correct)

When the remainder is 1

When converting the fractional part of a decimal number to another base, successive division is used.

False (B)

Using the remainder method, what is the first step in converting the integer part of a fixed-point number to a different base?

Separate the number into its integer and fractional parts.

In the remainder method, the new number in base 'r' is obtained by reading the remainders from the last remainder ______.

upwards Signup and view all the answers

How is the fractional part of a decimal number converted to another base?

Successively multiplying the fraction by the base (C) Signup and view all the answers

Which of the following best describes the foundation of digital logic?

Binary code, a series of zeroes and ones. (B) Signup and view all the answers

Digital logic design is primarily used for developing software applications.

False (B) Signup and view all the answers

Name three basic digital logic gate functions.

AND, OR, NOT Signup and view all the answers

In digital computers, data is stored in terms of ______.

digits Signup and view all the answers

Match the following terms with their descriptions:

Digital Logic = Basis of electronic systems using binary code. Radix = Defines the range of values a digit may have in a number system. Binary Code = A series of zeroes and ones representing opposite values. Signup and view all the answers

Why is the decimal system not convenient for machines at their fundamental level?

Machines handle information as on or off bits (binary). (B) Signup and view all the answers

Which fields are most closely associated with digital logic design?

Electrical engineering and computer engineering. (D) Signup and view all the answers

Digital logic designers only focus on the electrical characteristics of electronic components.

False (B) Signup and view all the answers

When using the nines' complement method for subtraction with decimal numbers, what adjustment is made after finding the sum of the first number and the nines' complement of the second number?

Add 1 to the sum, then drop the leftmost digit. (A) Signup and view all the answers

In binary subtraction using the method of complements, the ones' complement is obtained by inverting each bit, and the two's complement is then found by simply adding '1' to the ones' complement.

True (A) Signup and view all the answers

In the context of signed fixed-point numbers, what is the purpose of 'excess notation'?

Represent signed numbers without a separate sign bit Signup and view all the answers

In signed magnitude representation, the __________ bit indicates the sign of the number.

leftmost Signup and view all the answers

Match the following number representations with their corresponding characteristics:

Sign-Magnitude = Uses a sign bit and a magnitude part. One's Complement = Involves inverting all bits to represent negative numbers. Two's Complement = Adds 1 to the one's complement. Excess Notation = Adds a fixed value to represent signed numbers. Signup and view all the answers

What is the primary advantage of using the method of complements in binary arithmetic?

It simplifies subtraction by converting it into addition. (C) Signup and view all the answers

In an eight-bit signed magnitude representation, the number -12 would be represented as 10001100.

True (A) Signup and view all the answers

Why is dropping the '1' significant when performing subtraction using complements?

It indicates the result is positive and within range. Signup and view all the answers

What is the result of performing a one's complement operation on the binary number `10101010`?

<code>01010101</code> (A) Signup and view all the answers

In one's complement representation, the leftmost bit being 1 indicates a negative number.

True (A) Signup and view all the answers

What is a primary disadvantage of using one's complement representation for numbers?

It has two representations for zero. Signup and view all the answers

To form the two's complement of a number, you first complement all the bits and then add ______.

1 Signup and view all the answers

Which of the following is a key advantage of two's complement representation over one's complement?

Unique representation of zero (D) Signup and view all the answers

In two's complement representation, discarding the carry-out from the most significant bit during addition is always an error.

False (B) Signup and view all the answers

If you have an 8-bit number in two's complement representation, how many different numbers can be represented?

256 (A) Signup and view all the answers

Match the number representation with its characteristic:

One's Complement = Two representations of zero Two's Complement = Only one representation of zero Signed Magnitude = Explicit sign bit Signup and view all the answers

Which of the following statements accurately describes the behavior of an OR gate?

The output is high if at least one input is high. (B) Signup and view all the answers

A NOT gate, or inverter, can have multiple inputs and a single output.

False (B) Signup and view all the answers

In a logical diagram of an inverter, what symbol indicates the logical inversion?

circle Signup and view all the answers

A NAND gate is equivalent to an AND gate followed by a(n) ______.

inverter Signup and view all the answers

Match the logic gate with its corresponding function:

OR gate = Output is high if at least one input is high NOT gate = Inverts the input NAND gate = Output is the inverse of an AND gate NOR gate = Output is the inverse of an OR gate Signup and view all the answers

Given inputs x=1 and y=0, what is the output z of a NOR gate?

0 (C) Signup and view all the answers

The triangle symbol in a digital inverter represents the logical inversion.

False (B) Signup and view all the answers

Write the boolean expression equivalent to: "The output is high if the light switch is ON or if the motion detector senses movement."

light_switch + motion_detector Signup and view all the answers

In binary logic, 1 + 1 always equals 10, similar to binary arithmetic.

False (B) Signup and view all the answers

What are the three basic kinds of gates commonly used in digital logic design?

AND, OR, NOT Signup and view all the answers

A standard 14-pin Integrated Circuit (IC) package can contain four 2-input gates, three 3-input gates, or two ______ gates.

4-input Signup and view all the answers

Match the gate type with its corresponding function.

AND Gate = Output is 1 only if all inputs are 1 OR Gate = Output is 1 if any input is 1 NOT Gate = Output is the inverse of the input Signup and view all the answers

Flashcards

Digital Logic

The foundation of electronic systems represented by binary code.

Binary Code

A system using two symbols, 0 and 1, to represent data.